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What is the difference between the reflection of a complex number , say $3-4i$ about the x axis and the rotation of the complex number by $90°$ in the anti clockwise direction about origin ?

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    $\begingroup$ What are you asking? They are different numbers because they result from different operations. The first is finding the complex conjugate, The second is multiplying by $i$. Try drawing pictures. $\endgroup$ Nov 27, 2017 at 17:42

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The reflection about $x$ axis gives you the conjugate of the given complex number. But rotating by $90$ degrees in the counterclockwise direction is multiplying by iota. These two things are similar for a complex number lying on $x+y=0$ line, but not in general.

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